Solar center gravitational wave formation orbit optimization method for fuel-stability balance

Abstract

The invention relates to a fuel-stability balanced solar centroid gravitational wave formation orbit optimization method, which comprises the following steps of: firstly, establishing a high-fidelity dynamic model of a deep space spacecraft, and modeling relative motion of a solar centroid gravitational wave detection formation based on a differential orbit element to represent a decision variable of initial formation configuration; fuel consumption in a transfer stage is estimated through a fast fuel estimation algorithm, a fuel consumption-configuration stability global multi-objective optimization framework is constructed, and a corresponding fuel consumption-configuration stability Pareto leading edge surface is obtained; a fuel optimization framework with stability constraints is constructed based on an exterior point method, and a low-fuel-consumption configuration meeting the stability constraints is obtained; and finally, calculating the optimal fuel transfer corresponding to the low-burn-up configuration meeting the stability constraint by adopting an indirect method. According to the method, the fuel overhead in the transfer stage is considered while the configuration stability in the scientific detection stage is guaranteed, compromise optimization between the stability and fuel use is achieved, and about 15% of fuel can be saved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aerospace, and particularly relates to a fuel-stability trade-off heliocentric gravitational wave formation orbit optimization method. BACKGROUND

[0002] The existing gravitational wave detection technology mainly relies on ground interferometers, and due to the limited arm length and environmental interference, the observation frequency band is mainly concentrated in the high frequency band, and it is difficult to cover the low frequency band signal. In order to break through this limitation, space gravitational wave detection has become a new research hotspot. Space gravitational wave detection generally adopts a near-equilateral triangle formation composed of multiple spacecraft, and operates in a heliocentric orbit or a geocentric orbit. In order to meet the stringent requirement of formation stability, the existing technology mainly optimizes the initial formation to improve the geometric stability in the scientific stage. However, the existing technology ignores the fuel consumption in the transfer stage, resulting in excessive fuel consumption, which affects the mission life and feasibility. SUMMARY

[0003] The present application proposes a fuel-stability trade-off heliocentric gravitational wave formation orbit optimization method to solve the problem of excessive fuel consumption caused by ignoring the fuel consumption in the transfer stage in the prior art. The method ensures the stability of the scientific detection stage while considering the fuel consumption in the transfer stage, and realizes the compromise optimization between stability and fuel use, which can save about 15% of fuel.

[0004] The present application is realized by the following technical solutions:

[0005] The present application relates to a fuel-stability trade-off heliocentric gravitational wave formation orbit optimization method. First, a high-fidelity dynamics model of deep space spacecraft is established, and the relative motion of the heliocentric gravitational wave detection formation is modeled based on the differential orbital elements to represent the decision variables of the initial formation of the formation. Then, the fuel consumption in the transfer stage is estimated by a fast fuel estimation algorithm, a fuel consumption-formation stability global multi-objective optimization framework is constructed, and the corresponding fuel consumption-formation stability Pareto front is obtained. Then, based on the external point method, a fuel optimization framework with stability constraints is constructed to obtain a low fuel consumption formation that meets the stability constraints. Finally, the indirect method is used to calculate the fuel optimal transfer of the low fuel consumption formation that meets the stability constraints.

[0006] The heliocentric gravitational wave detection formation takes the Earth orbit as the reference orbit, selects a virtual main spacecraft near the reference orbit and makes it lag / lead the Earth by a certain angle. In the scientific detection stage, the virtual main spacecraft deploys the actual detectors in the detector formation to form an equilateral triangle formation, and the mission duration is a predetermined period . In the transfer stage, the detectors are released from the boundary of the Earth's action sphere, and the transfer time is limited Internally, it is propelled to the target configuration using continuous small thrust. .

[0007] The configurational stability includes: maximum arm length variation Changes in maximum respiratory angle Maximum arm length change rate Changes in the maximum formation center lag distance Among them: spacecraft and Changes in arm length , breathing angle , formation center lag distance The definition is based on the nominal arm length of the formation. nominal formation center lag distance and various spacecraft position vector .

[0008] The high-fidelity dynamic model of the deep spacecraft is as follows: ,in: and They are respectively the Sun and the Solar System The gravitational parameters of the planet, For the first The position vector of a planet, For spacecraft initial mass, for The thrust level of the thruster for The unit thrust vector, Standard gravitational acceleration, .

[0009] The high-fidelity dynamic model described above is defined in a heliocentric inertial coordinate system. In, such as Figure 3 As shown, The axis always points from the Sun's center of mass. The direction of the vernal equinox, The axial direction is the normal direction to the Earth's orbital plane. The direction of the axis is from shaft and The axis is determined according to the right-hand rule.

[0010] The aforementioned fast fuel estimation algorithm refers to: by analyzing the thrust duration... The iterative completion of a single spacecraft Minimum transfer fuel from the release position to the corresponding position in the target configuration A rapid estimation. The starting and ending states of the formation transition are respectively... and ,in: Let be the formation state vector, and For a single spacecraft The state vector contains position information. With speed information .

[0011] The quantitative analysis of the relationship between fuel and stability refers to: using the proposed stability index and fuel consumption, defining the stability objective function and the fuel consumption objective function respectively, analyzing the correlation between the two, and the influence of configuration decision variables on the two.

[0012] The aforementioned fuel optimal configuration design refers to: transforming the stability requirement into an inequality constraint, using the exterior point method to transform the constrained fuel optimality problem into a single-objective optimization problem with a penalty term, and finally obtaining the fuel optimal configuration that satisfies the stability requirement.

[0013] Technical effect

[0014] This invention addresses the problem of excessive fuel consumption during transfer due to the overemphasis on configuration stability in traditional methods for space gravitational wave detection missions. While focusing on configuration stability, it considers fuel consumption during the transfer process, employing a fuel consumption-configuration stability correlation analysis technique based on multi-objective optimization. Furthermore, it utilizes the exterior point method to construct a stable, low-fuel-consumption configuration design. Compared to existing technologies, this invention significantly reduces transfer fuel consumption while maintaining detector configuration stability. Numerical results show that it can save approximately 15% of fuel, which is significantly superior to existing technologies that only focus on stability. Attached Figure Description

[0015] Figure 1 This is a system structure diagram of the present invention;

[0016] Figure 2 This is a flowchart of the present invention;

[0017] Figure 3 Non-inertial frame of reference Schematic diagram and heliocentric inertial frame Schematic diagram;

[0018] Figure 4 This is a schematic diagram of the invention;

[0019] Figures 5-7 This is a schematic diagram of the simulation results for an example. Detailed Implementation

[0020] like Figure 1As shown in this embodiment, a heliocentric gravitational wave formation orbit optimization system involving a fuel-stability tradeoff is included, comprising: a configuration design unit, a fuel consumption estimation unit, a global optimization unit, a trajectory solving unit, a user input unit, and an output unit. The configuration design unit selects decision variables based on a differential orbit element model of relative motion to define the desired initial configuration of the spacecraft; the fuel consumption estimation unit, based on the current initial configuration, calculates the desired initial configuration of the spacecraft. The iterative fuel estimation obtains the minimum fuel required to transfer to the current initial configuration; the user input unit extracts the user's stability requirements for the configuration and the corresponding transfer fuel consumption balance requirements; the global optimization unit constructs a stability-fuel objective function based on user requirements and solves the stability-fuel Pareto front based on multi-objective optimization, describing the stability requirements with a penalty term, and obtains a stability-fuel trade-off design scheme based on single-objective optimization; the trajectory solving unit solves the corresponding optimal fuel transfer trajectory based on the stability-fuel trade-off design scheme; the output unit outputs the Pareto front solution, the stability-fuel trade-off design scheme, and the optimal fuel transfer trajectory.

[0021] like Figure 2 As shown, this embodiment presents a heliocentric gravitational wave detection formation orbit optimization method based on a trade-off between the stability of the above-mentioned system configuration and the consumption of transfer fuel. Taking the LISA heliocentric formation gravitational wave detection mission as an example, it specifically includes:

[0022] Step 1: Establish the configuration of the LISA mission spacecraft detection formation, specifically including:

[0023] 1.1 Constructing the relative motion equations of formation spacecraft based on differential orbit elements, specifically including:

[0024] i) Define spacecraft Corresponding classical orbital elements via spacecraft Compared to the virtual master spacecraft Differential orbit elements Representing relative position, where: For the semi-major axis, For eccentricity, For track inclination, Right ascension of the ascending node Argument near the arch point, It is the angle closest to the point.

[0025] ii) such as Figure 3 As shown, a fixed structure is introduced into the virtual master spacecraft. Rotating non-inertial frame ,origin Located in the virtual master spacecraft , The axis always points from the Sun's center of mass. direction, the normal direction of the orbit plane, the direction of the axis, the direction of the axis is determined according to the right-hand rule, the axis and the axis according to the right-hand rule, the radial, tangential and normal directions of the coordinate system, relative position components are specifically: , wherein: is the azimuth of the plane latitude, , , , , .

[0026] iii) When the orbit and the relative motion shape are known, the differential orbit elements are obtained, specifically: wherein: , , .

[0027] 1.2 Establish the decision variable for determining the initial configuration of the formation, specifically including:

[0028] i) According to the linear relative motion equation in step 1.1 and the differential orbit element inverse formula, the relative motion geometric parameter vector is determined, and the corresponding differential orbit element is obtained.

[0029] ii) Let satisfy the relationship: , and and satisfy: , then the initial configuration of the equilateral triangle formation with the nominal arm length is obtained, and the geometric parameter vector is: .

[0030] iii) Let the decision vector be: wherein: is the adjustment to the orbit number, is the non-singular orbit element, and the remaining decision variables are adjustments to the configuration. The adjusted geometric parameter vector is: .

[0031] Step 2, establish a fast iteration fuel estimation method, specifically including:

[0032] 2.1 Considering that the transition between near-circular orbits typically exhibits an "on-off-on" structure, the state transition matrix equation corresponding to the Lambert trajectory is constructed as follows: Two segments with durations of... and The full thrust arc is used to complete a single spacecraft Optimal fuel transfer for spacecraft The fuel consumption estimation problem is transformed into solving the sum of the two thrust durations. Using the corresponding Lambert orbit as a reference orbit and the optimal transfer orbit of the actual fuel as the external perturbation force, specifically: ,in: For spacecraft The state transition matrix corresponding to the Lambert trajectory. and spacecraft The state deviations relative to the reference orbit at the final and initial times, where: For the two successive velocity pulses corresponding to the Lambert transfer, and Let be the thrust acceleration in two consecutive thrust arc segments, and , These correspond to either the first or second thrust arc segment, respectively. Within the thrust arc segment, the mass... Over time change: .

[0033] 2.2 Solve step 2.1 iteratively, specifically including:

[0034] i) Spacecraft First, generate initial guesses for two thrust times. Let the number of iterations be... Take during the initialization of the iteration process Solve and Specifically: , where: function ,function , and For a point in time, For matrix The List.

[0035] ii) Update the Time interval in step Specifically: , where: parameters Let be the convergence ratio. .

[0036] iii) Repeat steps i-ii and update in each round. Until the termination condition is met: ,in: It is a relatively small tolerance value.

[0037] iv) Order for The stable value is determined by Approximately minimum fuel consumption .

[0038] Step 3: Determine the stability index requirements and fuel balance requirements based on user input. Specifically, define the upper bound of the stability index according to the user's stability index requirements. These correspond to the upper bounds of changes in arm length, breathing angle, rate of change of arm length, and hysteresis distance, respectively. The importance of fuel balance indicators is set according to the user's fuel balance requirements. It is used to constrain fuel balance among different spacecraft.

[0039] Step 4: Construct a stability-fuel multi-objective optimization problem and use the MOEA / D toolbox to search for the Pareto front, specifically: Where: configuration stability objective function Weighting coefficients The objective function for transferring fuel consumption is initialized to reflect the weights of each stability index. , It reflects the fuel balance among the spacecraft.

[0040] Step 5: Based on the user-defined stability metric requirements obtained in Step 3, establish a fuel optimization framework with stability constraints, specifically as follows: Where: constraint vector To meet user stability requirements, the problem is transformed into a single-objective optimization problem with a penalty term using the exterior point method: ,in: This refers to the penalty coefficient corresponding to the external penalty item. This is used to penalize violations of stability constraints. The differential evolution algorithm is employed to solve the above unconstrained single-objective optimization problem.

[0041] Step 6: Use the homotopy method to solve for the optimal fuel transfer trajectory corresponding to the low-fuel-consumption configuration that satisfies the stability constraints obtained in Step 5. Specifically, this includes:

[0042] 6.1 About Define homotopy index ,in: Scaling factor Construct the Hamiltonian to be the homotopy factor: , , These are the position-velocity related costate vectors. Let be the mass costate vector. The corresponding Euler-Lagrange equation is: .

[0043] 6.2 Based on the principle of minimum value The optimal thrust direction is obtained: And optimal thrust level: ,in: This is a switching function.

[0044] 6.3 Introducing new costate variables: And perform co-state normalization. Then, the target function is defined as: Wherein: the expected end position vector of the spacecraft when the formation deployment is completed. and velocity vector Determined by the output of single-objective optimization; by adopting from Gradually reduce to Homotopy method for solving optimization problems Obtain the initial costate vector for the fuel optimal control problem. .

[0045] Step 7: Output the Pareto front solution for multi-objective optimization obtained in Step 4. Step 5 yields a stable, low-fuel-consumption configuration optimized for a single objective. And the optimal fuel transfer trajectory and control rate corresponding to this configuration obtained in step 6.

[0046] Through specific simulation experiments, taking the LISA task as an example, the simulation was conducted, and the transfer start time was set to... The detector at Reach the target configuration and begin the period The scientific exploration mission is scheduled for [year]. The target formation configuration is [nominal arm length]. An equilateral triangle, nominal formation center lag distance for Assuming the relative speed increase at the boundary of Earth's influence sphere is zero, and the common starting position of the three probes is... ,in: The Earth's influence on the sphere's radius, It is a unit vector and takes The propulsion system employs continuous low-thrust propulsion, with a maximum thrust of... , specific impulse The initial mass of each detector is set to Optimize the decision vector The range of values ​​is defined as And its upper and lower bounds are respectively The physical quantities in the examples are adopted with dimensionless units: , , .

[0047] As shown in Figure 5 , the stability weight is set to and the fuel balance weight is set to during the simulation process. Step 4 obtains the non-dominated solution of the population containing 800 individuals, and the formed Pareto front indicates that there is a negative correlation between the stability index and the fuel consumption. The distribution of the Pareto optimal solution is used to study the conflict between and about which decision variables: first, the Sobol sensitivity analysis (Table 1) shows that the variables in about have the greatest contribution to , therefore, the distribution of and about decision variables in the Pareto optimal solution is plotted as shown in Figure 6 . The results show that there is a significant conflict between , and , and , with opposite trends.

[0048] The initial penalty coefficient of the optimization method of the present application is set to , and is gradually increased until the stability constraint is met. According to the allowed variation range of different stability indexes, three design cases are set (Table 2), in which: and are determined according to the LISA engineering requirements, and are set to , of the nominal value in cases 1-2, respectively, and case 3 is consistent with the LISA engineering requirements. The optimization algorithm adopts the differential evolution method, with a population size of 200, a crossover factor of 0.3, and a scaling factor of 0.5. The real fuel optimal transfer trajectory is calculated for the initial configuration, and the design results are shown in Table 3. The results show that cases 1 to 3 can meet the stability constraint, with an estimation error controlled within 13%, and compared with the traditional method (case A), about 15% of fuel can be saved. The real transfer trajectory of the spacecraft is shown in Figure 7 .

[0049] Table 1

[0050] Table 2

[0051] Table 3

[0052] Compared with the prior art, the method considers the fuel consumption required for realizing the corresponding configuration in the configuration design link, and constructs a fuel optimization technology with stability constraint based on the exterior point method, which significantly reduces the fuel consumption while ensuring the stability of the detector configuration. The numerical results show that about 15% of fuel can be saved, which is obviously better than the existing method which only focuses on stability.

[0053] The above specific embodiments can be adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present application. The protection scope of the present application is subject to the claims and is not limited by the above specific embodiments. Each implementation within the scope is subject to the constraints of the present application.

Claims

1. A method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff, characterized in that, First, a high-fidelity dynamic model of the deep spacecraft is established, and the relative motion of the heliocentric gravitational wave detection formation is modeled based on differential orbit elements to characterize the decision variables of the initial formation configuration. Then, the fuel consumption during the transfer phase is estimated using a fast fuel estimation algorithm, and a global multi-objective optimization framework for fuel consumption-configuration stability is constructed to obtain the corresponding Pareto front for fuel consumption-configuration stability. Next, a fuel optimization framework with stability constraints is constructed based on the exterior point method to obtain a low-fuel-consumption configuration that satisfies the stability constraints. Finally, the optimal fuel transfer corresponding to the low-fuel-consumption configuration that satisfies the stability constraints is calculated using an indirect method. The high-fidelity dynamic model of the deep spacecraft is as follows: ,in: and They are respectively the Sun and the Solar System The gravitational parameters of the planet, For the first The position vector of a planet, For spacecraft initial mass, for The thrust level of the thruster for The unit thrust vector, Standard gravitational acceleration, The high-fidelity dynamic model described above is defined in the heliocentric inertial coordinate system. middle, The axis always points from the Sun's center of mass. The direction of the vernal equinox, The axial direction is the normal direction to the Earth's orbital plane. The direction of the axis is from shaft and The axis is determined according to the right-hand rule.

2. The method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff as described in claim 1, characterized in that, The aforementioned heliocentric gravitational wave detection formation uses Earth's orbit as a reference orbit and selects a virtual master spacecraft near the reference orbit. To lag behind or lead Earth by a certain angle, during the scientific exploration phase, around Actual detectors in the deployed detector formation To form an equilateral triangle formation, the mission duration is the predetermined period. During the transfer phase, the probe is released from the Earth's interaction boundary and, within a specified time... Internally, it is propelled to the target configuration using continuous small thrust. .

3. The method for optimizing heliocentric gravitational wave formation orbits with fuel-stability trade-off according to claim 1 or 2, characterized in that, The configuration for establishing the LISA mission spacecraft detection formation specifically includes: 1.1 Constructing the relative motion equations of formation spacecraft based on differential orbit elements, specifically including: i) Define spacecraft Corresponding classical orbital elements via spacecraft Compared to the virtual master spacecraft Differential orbit elements Representing relative position, where: For the semi-major axis, For eccentricity, For track inclination, Right ascension of the ascending node, Argument near the arch point, It is a near-point angle; ii) Using a method fixed to the virtual master spacecraft Rotating non-inertial frame ,origin Located in the virtual master spacecraft , The axis always points from the Sun's center of mass. direction, axial direction The direction of the normal to the orbital plane, The direction of the axis is from shaft and The axis is determined according to the right-hand rule, resulting in... The radial, tangential, and normal directions of the coordinate system. Compared to The relative position components are specifically: ,in: for The horizontal latitude argument, and , , , ; iii) In When the orbit and relative motion shape are known, the differential orbit elements are obtained, specifically: ,in: , ; 1.2 Establish decision variables for determining the initial formation configuration, specifically including: i) Based on the linear relative motion equations and differential orbit element inverse formulas in step 1.1, determine the relative motion geometric parameter vectors of each spacecraft. Thus, the corresponding differential orbit elements are obtained; ii) Order Satisfying the relation: ,and and The following conditions must be met: Then the nominal arm length is obtained as The initial configuration of the equilateral triangle formation, The geometric parameter vector is: ; iii) Let the decision vector be: ,in: To Adjustment of orbital elements, For non-singular orbital elements, the remaining decision variables are adjustments to the configuration. The adjusted geometric parameter vector is as follows: .

4. The method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff as described in claim 1, characterized in that, The configurational stability includes: maximum arm length variation Changes in maximum respiratory angle Maximum arm length change rate Changes in the maximum formation center lag distance Among them: spacecraft and Changes in arm length , breathing angle , formation center lag distance The definition is based on the nominal arm length of the formation. nominal formation center lag distance and various spacecraft position vector .

5. The method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff according to claim 1, characterized in that, The aforementioned fast fuel estimation algorithm refers to: by analyzing the thrust duration... The iterative completion of a single spacecraft Minimum transfer fuel from the release position to the corresponding position in the target configuration The rapid estimation shows that the starting state and the ending state of the formation transition are respectively... and ,in: Let be the formation state vector, and For a single spacecraft The state vector contains position information. With speed information .

6. The method for optimizing heliocentric gravitational wave formation orbits with fuel-stability trade-off according to claim 1 or 5, characterized in that, The fast fuel estimation algorithm specifically includes: 2.1 Considering that the transition between near-circular orbits typically exhibits an "on-off-on" structure, the state transition matrix equation corresponding to the Lambert trajectory is constructed as follows: Two segments with durations of... and The full thrust arc is used to complete a single spacecraft Optimal fuel transfer for spacecraft The fuel consumption estimation problem is transformed into solving the sum of the two thrust durations. Using the corresponding Lambert orbit as a reference orbit and the optimal transfer orbit of the actual fuel as the external perturbation force, specifically: ,in: For spacecraft The state transition matrix corresponding to the Lambert trajectory. and spacecraft The state deviations relative to the reference orbit at the final and initial times, where: For the two successive velocity pulses corresponding to the Lambert transfer, and Let be the thrust acceleration in two consecutive thrust arc segments, and , Corresponding to the first or second thrust arc segment respectively, within the thrust arc segment, the mass Over time change: ; 2.2 Solve step 2.1 iteratively, specifically including: i) Spacecraft First, generate initial guesses for two thrust times. Let the number of iterations be... Take during the initialization of the iteration process Solve and Specifically: , where: function ,function , and For a point in time, For matrix The List; ii) Update the Time interval in step Specifically: , where: parameters Let be the convergence ratio. ; iii) Repeat steps i-ii and update in each round. Until the termination condition is met: ,in: It is a relatively small tolerance value; iv) Order for The stable value is determined by Approximately minimum fuel consumption .

7. The method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff according to claim 1, characterized in that, The quantitative analysis of the relationship between fuel and stability refers to: using the proposed stability index and fuel consumption, defining stability objective functions and fuel consumption objective functions respectively, analyzing the correlation between the two, and the impact of configuration decision variables on them, specifically: Where: configuration stability objective function Weighting coefficients The objective function for transferring fuel consumption is initialized to reflect the weights of each stability index. , It reflects the fuel balance among the spacecraft.

8. The method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff according to claim 1, characterized in that, The aforementioned fuel-optimal configuration design refers to: transforming stability requirements into inequality constraints, using the exterior point method to transform the constrained fuel optimization problem into a single-objective optimization problem with a penalty term, and finally obtaining the fuel-optimal configuration that satisfies the stability requirements. Specifically, it involves establishing a fuel optimization framework with stability constraints based on user-defined stability index requirements. Where: constraint vector To meet user stability requirements, the problem is transformed into a single-objective optimization problem with a penalty term using the exterior point method: ,in: This refers to the penalty coefficient corresponding to the external penalty item. To penalize violations of stability constraints, the differential evolution algorithm is used to solve the above unconstrained single-objective optimization problem.

9. The method for optimizing heliocentric gravitational wave formation orbits with a fuel-stability tradeoff according to claim 8, characterized in that, The optimal fuel transfer is obtained by solving the optimal fuel transfer trajectory corresponding to the low-fuel-consumption configuration that satisfies stability constraints using the homotopy method, specifically including: 6.1 About Define homotopy index ,in: Scaling factor Construct the Hamiltonian to be the homotopy factor: , , These are the position-velocity related costate vectors. For the mass costate vector, the corresponding Euler-Lagrange equation is: ; 6.2 Based on the principle of minimum value The optimal thrust direction is obtained: And optimal thrust level: ,in: It is a switching function; 6.3 Introducing new costate variables: And perform co-state normalization. Then, the target function is defined as: Wherein: the expected end position vector of the spacecraft when the formation deployment is completed. and velocity vector Determined by the output of single-objective optimization; by adopting from Gradually reduce to Homotopy method for solving optimization problems Obtain the initial costate vector for the fuel optimal control problem. .

10. A heliocentric gravitational wave formation orbit optimization system for implementing the fuel-stability tradeoff of any one of claims 1-9, characterized in that, include: The system comprises a configuration design unit, a fuel consumption estimation unit, a global optimization unit, a trajectory solving unit, a user input unit, and an output unit. Specifically: the configuration design unit selects decision variables based on a differential orbit element model of relative motion to define the desired initial configuration of the spacecraft; the fuel consumption estimation unit, based on the current initial configuration, calculates... The iterative fuel estimation obtains the minimum fuel required to transfer to the current initial configuration; the user input unit extracts the user's stability requirements for the configuration and the corresponding transfer fuel consumption balance requirements; the global optimization unit constructs a stability-fuel objective function based on user requirements and solves the stability-fuel Pareto front based on multi-objective optimization, describing the stability requirements with a penalty term, and obtains a stability-fuel trade-off design scheme based on single-objective optimization; the trajectory solving unit solves the corresponding optimal fuel transfer trajectory based on the stability-fuel trade-off design scheme; the output unit outputs the Pareto front solution, the stability-fuel trade-off design scheme, and the optimal fuel transfer trajectory.

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